Hi!

I have another question.

So 1 kcal of heat is added to 1.5 L of oxygen in a container at constant pressure. (1atm). Then volume increases to 3.1L. they want to know total energy change.

Now i think the formula is DH=DU + PDV
so what i did was DH = 1 kcal + 1atm(3.1-1.5) = 2.6 kcal...

its wrong... i don't know why please help!

thanks again!

To calculate the total energy change (ΔH), we need to consider the change in internal energy (ΔU) and the work done (PΔV) on the system.

You correctly identified the formula ΔH = ΔU + PΔV. However, there is a mistake in your calculation of the work done.

The work done on the system is calculated as PΔV, where P is the constant pressure and ΔV is the change in volume. In this case, the change in volume is (3.1 L - 1.5 L) = 1.6 L, not (3.1 L - 1.5 L) = 1.6 L.

Therefore, the correct calculation is:

ΔH = ΔU + PΔV = 1 kcal + (1 atm) (1.6 L) = 1 kcal + 1.6 atm·L

Since 1 atm·L is equivalent to 101.3 J (Joules), we can convert it to kcal:

1 kcal = 4184 J

1.6 atm·L = 1.6 × 101.3 J = 162.08 J

Converting J to kcal:

162.08 J × (1 kcal / 4184 J) ≈ 0.039 kcal

Therefore, the total energy change (ΔH) is approximately 1 kcal + 0.039 kcal = 1.039 kcal.

Hi!

It seems like you're on the right track with using the formula ΔH = ΔU + PΔV to calculate the total energy change (ΔH). However, there might be a small error in your calculations.

Let's go through the question again:

1. The heat added to the system is 1 kcal.
2. The initial volume (V1) is 1.5 L.
3. The final volume (V2) is 3.1 L.
4. The pressure (P) is constant at 1 atm.

To calculate the change in internal energy (ΔU), you can use the formula ΔU = q - PΔV, where q is the heat added to the system. In this case, ΔU = 1 kcal - 1 atm(3.1 L - 1.5 L).

Now, let's calculate ΔU:
ΔU = 1 kcal - 1 atm(3.1 L - 1.5 L)
= 1 kcal - 1 atm(1.6 L)
= 1 kcal - 1.6 atm·L

Now, to calculate the total energy change (ΔH), you need to add the work done (PΔV) to ΔU.

ΔH = ΔU + PΔV
= 1 kcal - 1.6 atm·L + 1 atm(3.1 L - 1.5 L)
= 1 kcal - 1.6 atm·L + 1 atm(1.6 L)
= 1 kcal - 1.6 atm·L + 1.6 atm·L
= 1 kcal

Therefore, the total energy change (ΔH) in this case is 1 kcal.

I hope this helps! Let me know if you have any further questions.